The implication (from OOtP) is that you are quite literally inside the pensieve;
But whether James really did take off Snape’s pants, Harry never found
out. A hand had closed tight over his upper arm, closed with a
pincer-like grip. Wincing, Harry looked round to see who had hold of
him, and saw, with a thrill of horror, a fully grown, adult-sized
Snape standing right beside him, white with rage.
Harry felt himself rising into the air; the summer’s day evaporated
around him; he was floating upwards through icy blackness, Snape’s
hand still tight upon his upper arm. Then, with a swooping feeling as
though he had turned head-over-heels in midair, his feet hit the stone
floor of Snape’s dungeon and he was standing again beside the Pensieve
on Snape’s desk in the shadowy, present-day Potion master’s study.
Snape had to enter the memory himself, grab Harry and then remove them both from it, back into the dungeon. Note that Harry's feet hit the stone floor. Clearly they weren't touching it before.
Later on, we get this exchange between Harry and Lupin:
‘I can’t tell him that, he’d kill me!’ said Harry, outraged. ‘You
didn’t see him when we got out of the Pensieve.’