Hockeyplayer - As a Charismatic Christian myself, I can offer you some issues to think about.
I find it hard to talk to other Christian friends about my denomination, let alone a boyfriend!
For example, the Holy Spirit usually fills me up when I'm in church and I'll start shedding tears. Other Charismatic Christians understand this experience, but if I talk to Christians of other denominations about this, they would think it's strange. This is one reason why I can't go to a church of another denomination, because the Holy Spirit won't fill me up there because He knows it would cause division between me and the church. I love the Holy Spirit so much that I would want Him to do what He desires, so that's why I only go to a charismatic church, so the Holy Spirit can fill me up whenever He wants, without worry about causing division.
Also, my brother is autistic. My family has been seeking a miracle for a long time. There are Charismatic churches that say, "May God's miracle rest upon your brother! Divine healing is part of the atonement, so believe it will happen!" There are conservative churches that say, "Don't expect a miracle. It might not be God's will." I tell these conservative churches that a Charismatic church that I attended pursued miracles, and many people got one. Their response was for me to watch out, because that church could be a cult. Do you see exactly how important it is for me to go to a Charismatic church? Because only they will pray for a miracle for my brother! I can't even talk to conservative churches about miracles because they think less of the gift of healing, and they believe that it's "cultic."
Back to your situation... Even though dating someone with a different denomination can work, I would ask that you think about a few things. Firstly, if one day the two of you get married, will you be attending church together? If so, then is one of you okay with switching to a church of a different denomination just to be with the other person? What about your future children? Which denomination will they be converted into? If one child has an illness (like my brother does), are you willing to go to Charismatic miracle services to get the healing? Or will you think those services are strange? Also, what if you catch your wife praying in tongues at home? Will you be uncomfortable? I know many non-Charismatics who are uncomfortable when they hear people praying in tongues...
Just because I can't date a Christian of a different denomination, doesn't mean you can't. I can't because the Charismatic denomination means too much to me. I want to go to a Charismatic church so the Holy Spirit will touch me! I want to pursue a miracle for my brother! I believe in divine healing in the atonement! I just cannot see myself dating a person who doesn't support my belief. I don't want to ever shut my mouth about the Holy Spirit, about miracles, about tongues, etc... If one of you you feel as strongly about your denomination as I do, then I would advise you two to think about dating someone with the same denomination. Otherwise, if you're both willing to drop the denomination debate, then it will work.
I also recommend that you talk to people from the Spirit-Filled/Pentacostal/Charismatic forum. Maybe learning more about our denomination will help you see things from our view, and thus understand your girlfriend more. I also think your girlfriend should learn more about your denomination.