We report on experimental results on dual-band high responsivity InGaAs/InP quantum well photodetectors covering both near and mid-infrared spectral regions. The mid-infrared detection relies on intersubband transitions. With changing well width both bound-to-bound and bound-to-continuum photodetectors have been demonstrated, thus determining the optimal design parameters for this materials system. The near infrared detection is via the usual interband absorption. The observed high responsivity values at high applied voltages are due to the combined effects of low excited-electron capture probability (related to the high mobility in these structures in contrast to the standard GaAs/AlGaAs ones) and of intraband impact ionization leading to an avalanche multiplication gain. To separate the two effects and unambiguously identify the latter, we performed noise measurements and carried out analyses using a newly developed theory.