In a normal conversation, the people who are not currently talking are very easily distracted from listening, by the thought of what they themselves are about to say. They can become preoccupied with retaining the memory of what they want to say, and looking for an opening for them to speak.
They are no longer able to focus on listening to the speaker.
I repeat, this is normal.
Now, over to your situation. Does your boyfriend, only interupt you, or does he interupt everyone?
If it is only you that he interupts, then the problem is within how you communicate together. I would suggest that you try the method that I have described here for communicating about important stuff:
I would also suggest that you try to analyse the conversation dynamic, when this happens, and possibly change that dynamic to lessen the impact of this problem.
For example, does your boyfriend tends to favour visual perception (he talks at a thousands mile an hour (because a picture paints a thousand words) and uses visual idiom - if you see what I mean), but you favour either aural perception (speak quite slowly, using high-faluting words (because you like how they sound) and use aural idiom - if you can hear what I am saying) or kinestetically (emotionally) perceptive (speak painfully slowly and hesitantly (because what you are about to say has to be processed by your emotions first) and use emotional idiom - if you can really get what I am trying to say).
In particular, if you are in the last category and he is in the first, he may be finding openings in your conversation, where you do not intend them.
If this is the case, he also probably finishes your sentences for you.
What you can do, is recognise the signs that he wants to say something, and give him the space to do so, before you carry on talking. For his part, he should practice discarding what he wants to say next when it pops into his mind, recognising that if it was really worth saying it will still be there when it is his turn to talk.
I hope that this helps.