I have about 30,000 Mileage Plus miles with United and around 26,000 Dividend miles with US Airways.

Can I combine the two sets of miles and use them to 'buy' a transatlantic flight on either (or another Star Alliance) airline, for which I would need 50,000 miles?

I have phoned both airlines and received fairly obtuse responses, they just say "miles are not transferable", yet their websites appear to suggest that miles earned on other airlines can be used.

Sorry if this is a real no-brainer of a question, but I am not really au fait with how these things work.

I have about 30,000 Mileage Plus miles with United and around 26,000 Dividend miles with US Airways.

Can I combine the two sets of miles and use them to 'buy' a transatlantic flight on either (or another Star Alliance) airline, for which I would need 50,000 miles?

You can use Dividend miles on all airlines in the star alliance but you can't combine your Dividend miles with your United miles for a single reward.