Wait until you are ready. You know your H better than anyone. I mentioned it when things were at their worst and got a positive response. Others have suggested it as a way to improve communication whatever the future holds. The weekends are only held a few times a year in any location. So you might want to check the schedule on the website, and bring it up about a month before a weekend. That way if he says yes, you can schedule it and it won't be too far in the future.
As for the Catholic part, it is offered as a non-denominational program. I am Jewish, and my husband is non-practicing, but was raised Catholic. He is particularly uncomfortable in Catholic settings. We both were able to sit through the priest's talks during Retrouvaille. I won't say it was my favorite part, but it did not detract from the overall good effect of the program. The religious perspective is presented in a non-denominational way. That is, yes, they do sometimes mention God or Jesus, but they don't preach gospel or Catholic doctrine. The religious segment is there, it is not the biggest part of the program, but it is there for those who can benefit from it. I could see within the group of 30 or so participants the weekend we were there, there were many people who really appreciated the priest's presence. That made me feel comfortable not interacting with the priest. He had plenty of other people to talk to.