A reconfigurable microwave photonic (MWP) multiband filter with selectable and switchable passbands is proposed and experimentally demonstrated, with a maximum of 12 simultaneous passbands evenly distributed from 0 to 10 GHz. The scheme is based on the generation of tunable optical comb lines using a two-stage Lyot loop filter, such that various filter tap spacings and spectral combinations are obtained for the configuration of the MWP filter. Through polarization state adjustment inside the Lyot loop filter, an optical frequency comb with 12 different comb spacings is achieved, which corresponds to a MWP filter with 12 selectable passbands. Center frequencies of the filter passbands are switchable, while the number of simultaneous passbands is tunable from 1 to 12. Furthermore, the MWP multiband filter can either work as an all-block, single-band or multiband filter with various passband combinations, which provide exceptional operation flexibility. All the passbands have over 30 dB sidelobe suppression and 3-dB bandwidth of 200 MHz, providing good filter selectivity.