I had to go check my neighbor's tree, and sorry it took me a while getting back here, but those leaves don't look like ours! Now, we could be wrong that this tree is mulberry, or there could be another variety or more than one!
Here is what our leaves look like, with some of the fruit. Wind was blowing pretty hard so it was difficult to get a clear picture:
Our leaves are not lobed like those in Catmint's picture, but the fruit looks the same.
