I've been looking for flights to and from Spain..so far I've found Air Europa to be one of the best priced...Of course I'm sure it depends on the time of year and how far ahead you book...
Air Comet is another airline that flies direct from the DR to Europe, but it seems to be a bit more pricey.
British Airways flies to various destinations from the DR but always stops in Miami it looks like. Not sure on the prices...but they have EXCELLENT service. I just flew with them from Canada to Europe and got back a few days ago. I travel alot, and I have to say British Airways has some of the best service I have ever experienced.
Where in Europe are you wanting to get to?