Above I have plotted few Planck's radiation contribution:
The violet is due to CMBR, Green is due to Milky way Galaxy, and Blue is due to contribution from both.
One way to resolve out CMBR is by modeling milky way from higher frequency of the graph since CMBR contribution is negligible at higher frequency. At particular direction one can associate temperature due to Milky way by setting a high pass frequency. Then one can subtract this temperature contribution at lower frequencies where CMBR contribution is significant. This is the one of the way probably not the best, but doable.
Note1: The graph is not from actual data. It is just for explaining how to go about it.
Note2: What should be high pass frequency will be a good question. With good arguments one can decide what should be the high pass frequency. And there's always way about it.