On the plus side, your son talked to you before he wanted to have sex, and after he started. You had a discussion about protection, which is good. Hopefully this included very factual information about both pregnancy prevention and disease prevention. (Yes, they are telling you that they want to be "the first" for each other, but who knows if that is true?) So your talks should have included a discussion of condoms as PART of the contraceptive picture (not all), but they will also help with prevention of sexually transmitted infections.
But there are details missing from your story. Where are they having sex, if it's not in your house? At her house? At friends' houses? In a car? Behind the school? If the girlfriend is being dropped off at your house every weekend, should we assume the sex is happening at your house? So you don't have an open door policy with your children? What do your other children think is going on?
And how are they affording the birth control and protection you and your husband advised? You seem to think the other mom has an inkling, but you don't know for sure because you haven't talked to her. I agree with you that if you just say no, they can't ever see each other again, they will sneak around. But that doesn't mean you have to provide a bed for them to have sex in. You don't feel this is right for a teenager, and you also have 2 other teens in the house who are either aware of what's going on because they observe it, or they are getting info from their brother. And if your teen and his girlfriend are talking about it, then other kids at school know about it. If they break up, this legacy stays with them.
So I would say, yes, you talk to the other parents. You make a plan to take both kids to the doctor so they get some education and have a chance to ask medical questions from an objective professional.
You also have a very strict talk about sexting and you have access to your son's cell phone so you can check for photos which stay on the internet forever. If your son will not give you his password, take the phone away. It's a privilege only for those mature enough to handle it. They also need to have access to part-time jobs so they can afford their contraception. Take them to Planned Parenthood or another reputable clinic, again so they can get good information and understand the repercussions.
There's a difference between accepting the reality of his sexual activity and approving of it. The decision-making portion of kids' brains isn't fully developed until age 25 or so. They don't understand that, and they don't fully understand consequences. So it's your job to step up and set strong parameters.