It is the person who has contracted the disease to protect their partner. Take the great medications that are available now to control breakouts and protect your spouse and any other lovers.
Any future lovers should be told so they also can take precautions. You're in a tricky state with your mate because if you have never had to use protection and suddenly have to, you will have to come up with some story if you choose to not tell them the truth.
If the STD were any of the others that can destroy your spouse, then you must inform him. If you don't, your doctor may push you because there are cures for those such as siphilis, gonnareha, etc..
If your marriage is strong enough to stand, in spite of the infidelity, then the mate should be told. It is still your choice now, but if your mate contracts it from you, the truth will come out anyway.
Best of luck.