Austin tells TMZ ... he was sitting on his couch Sunday night while Lexy was upstairs taking a bath when they both heard gunshots ... and then they felt their house rattle.

He says they checked their surveillance cameras and heard a gun being loaded, cocked, and fired. He called police, who came and quickly discovered a bullet hole in the home's exterior.

TMZ obtained a photo of the bullet hole ... as well as home security footage in which you hear the gun discharge. You can't see who fired the shot in the video.

Police in Nashville tell TMZ ... officers responded to the couple's home over the weekend for a shots fired report. We're told no arrests have been made and the case remains under investigation.

Austin tells us it's "incredibly unsettling" knowing someone fired a gun at their home in the middle of the night with his pregnant wife inside. He has no idea who did it.