Your infidelity has ruined your chance to have an appropriate friendship with this other person. Do him a favor and give him lots of room, because you are a near occasion of sin for him and a reminder of his profound betrayal of your husband’s trust. It is good that he wants to put his offense against your husband far behind him. You should, too. You betrayed your husband’s trust, too, and the degree to which you are “growing apart” or not doesn’t change that.
One thing at a time. You and your husband, both baptized, married according to the laws of the Church…that is a sacramental marriage. Don’t start dreaming about the other Catholic sacraments while you plan to commit sacrilege against the Catholic sacrament you have. Don’t start dreaming about converting in public when you are holding back from a conversion of heart from what I gather by your vague description was a mortal sin. I do not want to be too hard on you, but the evil one is trying to poison your desire to convert from the very start. Don’t let that happen!
You aren’t Catholic yet, but you can definitely approach a Catholic priest and ask for advice about your desire to join the Church and how to try to return to fidelity to your marriage vows. It is not at all uncommon, though, for lukewarm spouses to experience a conversion of their own when the rest of the household converts. It doesn’t always happen, but these issues are something that a parish with an RCIA program can address.
If you don’t know what geographic parish you belong to–Catholic dioceses are broken up into parishes like states are broken up into counties, so based on your home address you do actually have a “home church”–you can call the office of your local diocese and find out. If the bishop allows the faithful latitude concerning which parish they will be given the rights of the sacraments simply by virtue of regular attendance or their choice of registration, they will tell you about all of the parishes in your area, and not just your geographic parish, but that will differ from one diocese to the next.
Please do your soul a favor, though. Renounce the sins you have allowed yourself against your marriage, your husband, this other Catholic whom you purport to care about, and God. Repent from your adultery and your covetous thoughts entirely. You no doubt have heard the passage “whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is gracious, if there is any excellence and if there is anything worthy of praise, think about these things” (Phil. 4:8). Make yourself a list of thoughts that fit that description, and when thoughts of this person who attracts you to illicit things comes into your mind, substitute a good thought, instead. It will take awhile, but you can break the habit or at least diminish it greatly if you ask for God’s help and work at it.
Hang in there. God has tender mercy on the contrite heart. He doesn’t desire that you die, but that you live.