Precise knowledge of hadron production rates in the generation of neutrino beams is necessary for accelerator-based neutrino experiments to achieve their physics goals. NA61/SHINE, a large-acceptance hadron spectrometer, has recorded hadron+nucleus interactions relevant to ongoing and future long-baseline neutrino experiments at Fermi National Accelerator Laboratory. This paper presents three analyses of interactions of 60 GeV/c π+ with thin, fixed carbon and beryllium targets. Integrated production and inelastic cross sections were measured for both of these reactions. In an analysis of strange, neutral hadron production, differential production multiplicities of KS0, Λ and Λ¯ were measured. Lastly, in an analysis of charged hadron production, differential production multiplicities of π+, π−, K+, K− and protons were measured. These measurements will enable long-baseline neutrino experiments to better constrain predictions of their neutrino flux in order to achieve better precision on their neutrino cross section and oscillation measurements.