Is it possible to keep a somewhat relationship with your family if they are witnesses and have a "worldly" girlfriend?
It's depends on the parents, but it's very unlikely. Most parents do not want to loose a relationship with their adult children, but the religion teaches the shunning is for their own good. They believe that everyone who isn't a JW is going to die at Armageddon, which is any day now (and has been for more that a hundred years ). This is what you are up against, it is a cult and they don't play fair.
That he is going to the convention is not a good sign that he has not actually broken free of the mind control. If you try to talk to your love about these things I can pretty much guarantee his conditioned fear will come up and his mind will shut down to you. I left this religion, knew it wasn't "the truth" but didn't seek out any information about it on the internet for eight years. It took that long for the fear of "apostates" to go away. It was only then I realized how I had been deceived. If what the Watchtower taught was "The Truth" why were they so afraid of outside information? Real truth stands up to scrutiny, it's only lies that do not.
Please inform yourself about cults and how they work, it will give you an idea of what you are up against. We get people on this discussion board all the time who are in this exact same situation, they usually end up with a broken heart, sad to say.
I would recommend reading Steve Hassan's book, Combatting Cult Mind Control. If you don't want to invest in a book, a brief explanation of cults is at howcultswork.com.