A design of near- to mid-infrared tunable multichannel filter (MCF) based on the doped semiconductor-dielectric photonic crystal (PC) heterostructure is proposed. Here, a strongly extrinsic semiconductor, n-type germanium (n-Ge), is used as one of the constituent layers. The occurrence of multichannel feature originates from the negative-permittivity in the highly doped n-Ge. The existence of tunable feature is due to its concentration-dependent permittivity. It is of interest to find that, in such MCFs, the number of channels, i.e., the number of resonant transmission peaks, is directly related to the stack number, and these peaks are located within the pass band of the ideal host PC. The multiple channels are blueshifted as the impurity concentration increases. This design suggests an alternative of engineering the pass band for realizing an MCF instead of engineering photonic band gap in a PC containing photonic quantum well structure as a defect. Our analysis is made based on the transfer matrix method together with the Bloch theorem.