Block transmission with zero padding (ZP) and cyclic prefix (CP) are becoming attractive procedures for their ability to eliminate both inter-symbol interference (ISI) and inter-block interference (IBI). In this paper, we present joint blind channel estimation and interference suppression for single carrier block transmission using both ZP and CP. The proposed estimators take the same form, which gives flexibility for application to either one with minor changes. Our approach uses a generalized multichannel minimum variance principle to design an equalizing filterbank. Channel estimate is then obtained by deriving an asymptotically tight lower bound of the filterbank output power. Numerical examples show that the proposed schemes exhibit low sensitivity to unknown narrowband interference and compare favorably with subspace blind channel estimators.