Not likely, at least while both are still functioning as religious buildings. Not only do those three groups tend to not agree ideologically when it comes to religious issues, but the construction of their holy buildings requires differences in the structures themselves. For example, most churches are built in the shape of a cross (And many doctrines state it must be in the shape of a cross), and contains a depiction of Christ, usually being crucified, as well as other important biblical figures. Mosques, however, cannot have any form of illustrations or depictions of religious figures because they consider it idolatry. In order for one to comfortably practice their faith, you offend the other. They also require different consecration rites and rituals which, while not necessarily offensive to the other, can interfere with them or infringe upon the other building.

There are instances where religious buildings have served as multiple different holy buildings at different points in their history, such as the Hagia Sophia, but none that have actively served simultaneously to more than one outside of a symbolic role (The HS is currently not an active mosque, and is instead a historic site.)

Also, most people want to worship their religion with people who feel the same way they do, and not be butting heads (either actively or passively, with good or ill intent) with another who can think radically different from them. It's usually just better for all parties involved to build them separately at separate locations and allow them to do their own thing without possibly interfering with each other.

There are a few shrines and holy sites in the Middle East that, historically speaking, often had separate areas or buildings on the same site, since the three Abrahamic religions each held the site holy for different reasons.

Probably the best example of this still extant is the Tomb of Samuel, where there is a three-story buildings with each faith having it's own floor. There can be disputes over who gets to be closer to the sky or ground, but it's generally worked out pretty well, at least locally.