Is it normal that i still love my man even though he still sees his x?

My boyfriend and I love each other a great deal. He treats me like a queen, tells me constantly how beautiful I am and how much he loves me, but he keeps seeing his ex! They have a dog together and he says he sees her just to see the dog, but I found out that he will stay there for days, sleeping over! He says they are just friends, he sleeps on the couch and that I have nothing to worry about. Right now we have a long distance relationship and the ex lives close to me and I discovered that before he comes to stay with me for a while during his vacation time and after he leaves, he goes to stay with the ex for a couple of weeks.
I know I should kick him to the curb, but I want to believe there is nothing going on because I love him so much. I have confronted him about staying with her and he gets angry and acts like I am being unreasonable and jealous when he just wants to spend time with his dog that she kept. (I think she kept the dog as her ace up her sleeve, because she knew he would want to see the dog all the time. He loves the dog. Also he left her, she didn't leave him, so I think she wants him back).
I can't stop loving this man and if it weren't for the ex, things would be perfect.