Sometimes it's easier to see what happens if you eliminate the non-reacting species. In this case, the metallic cations don't do much, so you can write the anions only:
H2PO4- + HCO3- --> HPO42- + H2CO3 --> HPO42- + H2 + CO2
A proton has been transfered from the dihydrogenophosphate anion to the hydrogenocarbonate anion. The carbonic acid thus formed is unstable and decomposes to water and carbon dioxide.
So there are actually at least two reactions occurring. I don't know what they are 'officially' called like, but as long as you figure out what happens, any teacher should be happy enough.