My husband of 13 years just told me that he cheated on me with a coworker of ours

My husband of 13 years just told me that he cheated on me with a coworker of ours because my doctor told me I might have an STD and to talk to my husband about it.

He claims he gave her oral sex about 4 years ago and that is all that happened. He also admits to kissing another woman at a bar about 8 years ago.

During the past several years I have asked him repeatedly if he had cheated on me because his behavior was secretive and suspicious and he always told me that he never had and never would.

I feel like I am in the twilight zone and I don't know what reality is anymore. Our relationship has actually been really good for the last couple years, but finding out about the repeated lying that happened during that time period makes me doubt if it really was good.

I wonder if he is still cheating on me, if he doesn't love me but can't find the guts to tell me that, or if he is just staying with me because of our kids.

I have told him I would be open to discussing an open relationship, but I cannot abide the lying because it is disrespectful to me and our relationship, as well as dangerous (I'd rather not get an STD from his unknown extracurricular activities, obviously). I don't know if my husband is still cheating with this co-worker. Please help