Laura - just in case you don't know this already - NEVER take fashion advice from a man.
So, to actually answer your very good question - there are variations in June as far as weather and variations in weather in the two cities you mention. There is a chance that you might get some cooler and/or rainy weather in Venice, so pack some kind of lightweight sweater, shawl, etc. I've used both during summer trips,especially at night.
Since you DO want to look nice, honeymoon pictures and all, and it sounds like you aren't doing any real hiking, bring lightweight casual summer clothing. I always bring longish (at least knee length) skirts to be able to visit churches like St. Peter's. I prefer skirts - again, summer style, casual - as does my 20 something daughter, but you can certainly wear capris if that is more your style. You also need to cover your shoulders during church visits, so if you are wearing cami tops or something like that, just bring the lightweight shawl/scarf with you in your purse. You can put it on top before you go in. And, unlike France, NOT everyone will be wearing black all the time- too hot. Make sure your husband knows to also bring at least one pair of lightweight long pants to wear for major church visits.
The BEST thing about traveling in the summer is that women's clothing is so lightweight and packs so easily that you can bring more than you may think and still go with the 1 carryon. The only trouble most women have is with shoes, especially thinking they may want to have some special evenings. But you really need to limit yourself on this - I always do 2 pair wear 1, pack 1. But you may be able to get 1 more pair in - maybe a cute, but flat sandal. I prefer clunky (not very pretty) walking sandals. I can wear them with both skirts and capris.
Don't know what your laundry prospects are - I bring at least enough to last 1 week and then wash, mainly the shirts. Congrats -have fun!