The rules appear to be different between different jurisdictions, and there does not seem to be much detailed official information about how these matters worked in Britain, the setting of the main Harry Potter novels. Pottermore does not have an article about the International Statute of Wizarding Secrecy, which presumably sets the minimal conditions for secrecy that wizards have to obey everywhere.
However, in certain locations, the rules could be quite a bit more strict—to the extent that wizards dating muggles was simply forbidden outright. For instance, n North America, Rappaport’s Law enforces much more draconian restrictions on sharing information between wizards and muggles. Quoting Pottermore:
Rappaport’s Law enforced strict segregation between the No-Maj and wizarding communities. Wizards were no longer allowed to befriend or marry No-Majs. Penalties for fraternising with No-Majs were harsh. Communication with No-Majs was limited to that necessary to perform daily activities.
The article on Rappaport’s Law also provides a little bit of detail about the generalities of communication between wizards and muggles in Europe.
In the Old World, there had always been a degree of covert cooperation and communication between No-Maj governments and their magical counterparts. In America, MACUSA acted totally independently of the No-Maj government. In Europe, witches and wizards married and were friends with No-Majs; in America, No-Majs were increasingly regarded as the enemy.
The Harry Potter Wiki article contains a bit more information, presumably gleaned from a variety of published sources. The following information is attributed to to Harry Potter and the Deathly Hallows, chapter 16 ("Godric's Hollow"):
Several magical families were attracted to small villages and hamlets, where they could start their own communities, for mutual support and protection, alongside more tolerant and sometimes Confunded Muggles. Some of the most celebrated of these half-magical wizard villages of Tinworth in Cornwall, Upper Flagley in Yorkshire, Ottery St Catchpole in Devon, and Godric's Hollow in the West Country date back to then.
Without attribution, the article also includes this note:
Originally, Isobel McGonagall followed the Statute by concealing her magical heritage from her Muggle husband, Robert McGonagall Snr. However, when their first daughter Minerva was exhibiting magical powers, Isobel was forced to break the Statute and reveal to her husband the existence of the wizarding world. This shows that wizards and witches with Muggle spouses may reveal the magical world under such circumstances. It was for this reason that Minerva refused to marry Dougal McGregor, fearing to bring up her magical heritage.
This passage blatantly contradicts itself as to what constitutes a violation of the Statue, but it does suggest that under certain circumstances, it might not eve be permissible for wizards and witches to inform their spouses and other first-order relations of their magic-using status. However, this also seems to contradict a great deal of material from the novels, which clearly indicate that the muggle parents of Hogwarts students are fully aware of the existence (if not necessary the detailed nature) of the wizarding community.