In our case, I was the one who converted to the Catholic faith. My husband is quite happy at the United Church.
I used to think that I was going to try to attend both, but on the advice of my priest, I am attending only the Catholic Church. My priest’s reasoning was that people in the Protestant church might get confused and either think that I didn’t actually convert to the Catholic faith (which would be a confusing witness to others) or else think that Catholics are generally allowed to go to Protestant churches (which is not true) and start trying to encourage their other Catholic friends to come, by saying, “Oh, but “J” is Catholic, and she comes to our church!” - which could lead to who knows what kind of trouble.
So, I followed his advice, and going only to Catholic Mass is working out just fine for us.