I think Severus Snape saw Dumbledore pretty much as Harry saw Dumbledore too. The picture is the wise old man with the friendly attitude, the one to know what's right and wrong. Furthermore the very talented wizard who never failed neither in his magic abilities nor in his social or personal treatment of people and the strategist to defeat Voldemort. This is a very positive picture in itself. If the picture of Dumbledore is reality and survives book 7 is another topic.
Severus was (beside the goal of safeguarding Harry) seeking the appreciation and the advice of Dumbledore for his abilities, his actions, his loyality towards Dumbledore in fullfilling Dumbledores requests, even more seeking the encouragement that he's on the right way to do the right thing, at least for keeping Harry save. If Severus got encouragement, advice and appreciation is another topic, but he would have accepted advice and teaching from Dumbledore and does still in book 7 for defeating Voldemort.
The difference between Harry and Severus in my opinion is that Harry got the appreciation, respect and encouragement by Dumbledore, but Severus didn't (at least not in that frequency nor any emotional depth nor the advice to correct faulty behaviour without risking cover of a spy).
But still Severus was very positive about Dumbledore (similar to Harry) and likely realised very late (end of book 6) what Dumbledore was playing. He hasn't seen himself as a chess pawn, nor Harry, nor anybody else, because he thought he (and all the other) matter to Dumbledore - also as a person - at least to keep Harry save.
Further evidence:
He's spilling his own bad impression of Harry to Dumbledore (after meeting Harry first time in book1, but revealed in book 7). Severus isn't correct with his opinion, but that was his opinion at this very moment. Would you do if you didn't have a positive feeling about somebody and trust that he doesn't believe you at least a little bit? I wouldn't. So Severus is postive about Dumbledore in telling him about a very emotional situation, the first meeting of the boy to be protected, but also the child of his love and enemy.
Harry hears from Dumbledore in book 1 that Severus just saved Harry, because James did save Severus too. In book 3 Harry tells it to Severus and Severus is disappointed, because he would have assumed that Dumbledore is a bit more near the truth in Severus eyes. Severus did expect that he matters to Dumbledore and knows his thougths and hurt feelings about the Marauders, even if it comes to his schooldays, because Dumbledore matters to him and he never revealed Lupins secret in the past either!
In book 2 the petrified cat is found and Dumbledore and Severus know both that Harry doesn't tell the teachers all he knows about. Severus is upset, because he thinks his opinion matters to Dumbledore, but Dumbledore lets Harry escape without any questioning. So Severus feels at least betrayed in his abilities and his actions to find the truth, because Dumbledores opinion matters to Severus.
In book 3 Severus is outright beside himself, surely a difficult situation for Dumbledore too, even under the pressure of actions and Fudge in the room. But what makes Severus most hurt is if Dumbledore answers that his mind is still as good as it ever was, when beeing asked about Sirius beeing capable of murder at sixteen. Severus is finally seeking some appreciation or understanding from Dumbledore for the actions of the day, but gets a kick in the face (verbally). So Dumbledore matters to Severus.
In book 4 Severus is even more cruel to the students, even more bad tempered than usual. The relation is broken between Dumbledore and Severus (because of Severus emotional outbreak in book 3) and just restored at the end of book 4, when Severus returns to the death eaters as spy. Severus is defending Dumbledore for having made no mistake with the hexes around the goblet of fire, he's blaming Harry, but defending Dumbledore against the accusations of Karkaroff etc. He seems even to be shattered when Moody is searching his office, and mentions that Dumbledore used to trust him. He's right beside Dumbledore after the killing of Cedric. He's telling Dumbledore about the dark mark getting stronger. It means Dumbledore and beeing in Dumbledres good books as a person matters to Severus.
In book 5 Severus takes the challenge to teach Harry Occlumency. It's not just an emotional journey to Harry, but also to Severus. He sees through the memories of Harry flashes of Lily (and James at her side), he finds out that Harry was also once on a tree - trapped by a dog (similar to his hanging upside down by James), he's not amused of seeing a death eater beeing tortured by Voldemort. In general I think he does a good job in teaching Harry, but their relationship is so damaged in the meantime, that he's hardly a chance to be successful. But he does it for Dumbledore and he seems also to report truly about the training of Harry including the end of it. So Dumbledore matters to Severus ...
In book 6 he tells Bellatrix. In book 6 he's more defiant, more pressing to get to know what Harry knows. He knows Dumbledore will die, it's his last chance to ask him, but he doesn't get the answer, only another difficult task to bring the bad news to the boy. Dumbledore matters to him, he would have liked to save his life or to "buy more time" (see book 7), he would have liked to even take more and other tasks, but not the one to kill Dumbledore, not the one to bring Harry the final message ... because Dumbledore matters to Severus ... and in my opinion more than just the strategic thinker in defeating Voldemort.
Severus was of course never friendly and often bad tempered and just able to show resentment, anger, hate, mockery, but still Severus would have liked a father figure and trusted advisor in Dumbledore. But without feelings of father/son/grandfather/grandson/mentor or tutor it was finally just a strategic alliance between two lonely men, no matter how positive Severus saw Dumbledore as a person.
So Snape isn't positively referring to someone about Dumbledore (except Bellatrix and Harry on Occlumency lessons); or showing a positive feeling about him via Pensieve, but from the course of action s he was very positive and trusting towards Dumbledore I would say until the very end, but at least until almost end of book6.
