When I was a cop we wore leather uniform jackets in the winter. We also wore body armor under them, because unless cows have been genetically engineered since the 80s, leather isn't bulletproof.
If you are concerned about penetration, use a flat-point bullet rather than a hollowpoint.
Buffalo Bore sells a 100gr hard-cast flat-nosed lead bullet for the .380 that should penetrate just fine, leather jacket or not. The hole won't be any bigger than that left by a 9mm, .38, or .357 that doesn't expand, nor will it be any smaller.