We use data from the Tenerife 10-, 15- and 33-GHz beam-switching experiments along with the COBE 53- and 90-GHz data to separate the cosmic microwave background (CMB) signal from the Galactic signal, and create two maps at high Galactic latitude. The new multi-MEM technique is used to obtain the best reconstruction of the two channels. The two maps are presented, and known features are identified within each. We find that the Galactic contribution to both the 15- and 33-GHz Tenerife data is small enough to be ignored when compared with the errors in the data and the magnitude of the CMB signal.