We investigate the optimum transmit power allocation problem for the multi-band relay (MBR) channel. MBR is defined by a source node, a relay node, and a destination node communicating over multiple orthogonal bands. We focus on three relay transmission schemes: amplify-and-forward (AF), estimate-and-forward (EF), and compress-and-forward (CF) and study the optimum transmit source and relay power allocations to maximize the instantaneous achievable rate. We formulate iterative algorithms to find the power allocation for each scheme. It is shown that CF is always better than EF and AF. We observe that when the source-to-relay links are better than the source-to-destination links, EF and AF perform equally well. When the source-to-relay links are worse than source-to-destination links, AF performs better than EF.