Leo and his model girlfriend are enjoying each other's company in Italy ... so much so, Leo snuggled Vittoria in his arms on a staircase at an ancient church as he sipped a hot drink and took in the sights.

We haven't seen Leo and Vittoria this lovey-dovey before ... so the photos are super interesting.

LD and VC did some sightseeing together too ... visiting the Basilica of San Clemente before getting romantic at the Church of San Bonaventura al Palatino, which overlooks the Colosseum.

Leo did the Instagram boyfriend thing too ... snapping a bunch of photos of Vittoria and his mother, Irmelin Indenbirken, from their scenic church perch.

Vittoria looks super comfortable around Leo's mom here ... because Irmelin grabbed the camera and took a couple shots of her and Leo hugging on a balcony.