I'm involved with a woman in a poly marriage, the gender-mirror image of what you are doing.
She asked if I would be willing to meet her husband. Right from our first date she had told me about his personality, so I had a sense of what to expect (intelligence, charm, generosity). As it turned out, I like him a lot.
The sense I got was that, as Autumnal wrote, it was very important to her that I meet her husband. And I've come to recognize that it was very useful for me, too: when I run into him coming and going I can greet him with genuine pleasure and friendship. Knowing him makes EVERYTHING easier.
Yes, as a secondary partner you have "rights." You should not be asked to do things which make you uncomfortable or frightened. Your needs should be considered: for instance, your BF should not cancel dates at the last second because his wife changed her plans.
On the other hand, a considerate secondary should not do things which disrupt the primary relationship except in dire need. You should recognize that he loves her, and her love for him is one of the things which allows him to care for you as well.
Be gentle and thoughtful of both the other people in the relationship and you will have a better chance of helping it successful for everyone.
Some things may be off-limits to you, and that must be respected by the others. They may also have things that are off-limits, but they're going to have to make you aware of those. For instance, the couple I'm involved with avoids smooching when I'm around, and I honor that by not being physical with her when he's around either. That was never spelled out; it's just something picked up along the way.
These are just examples from the relationship I'm most familiar with. I know that many people on this board have very different ones, with different boundaries and different shapes. But as Autumnal wrote, if you don't know then you need to ask.