For over a century, the identification of high-energy cosmic ray (CR) sources remains an open question. For Galactic CRs with energy up to 10¹⁵ eV, supernova remnants (SNRs) have traditionally been thought the main candidate source. However, recent TeV γ-ray observations have questioned the SNR paradigm. Propagating CRs are deflected by the Galactic magnetic field, hence, γ-rays and neutrinos produced via inelastic hadronic interactions are the only means for unveiling the CR sources. In this work, we study the γ-ray and neutrino emission produced by CRs accelerated inside Galactic jets of stellar-mass black holes in X-ray binaries (BHXBs). We calculate the intrinsic neutrino emission of two prototypical BHXBs , Cygnus X–1 and GX 339–4, for which we have high-quality, quasi-simultaneous multiwavelength spectra. Based on these prototypical sources, we discuss the likelihood of the 35 known Galactic BHXBs to be efficient CR accelerators. Moreover, we estimate the potential contribution to the CR spectrum of a viable population of BHXBs that reside in the Galactic plane. When these BHXBs go into outburst, they may accelerate particles up to hundreds of TeV that contribute to the diffuse γ-ray and neutrino spectra while propagating in the Galactic medium. Using HERMES, an open-source code that calculates the hadronic processes along the line of sight, we discuss the contribution of BHXBs to the diffuse γ-ray and neutrino fluxes, and compare these to their intrinsic γ-ray and neutrino emissions. Finally, we discuss the contribution of BHXBs to the observed spectrum of Galactic CRs.