We present the discovery and characterization of two warm mini-Neptunes transiting the K3V star TOI-815 in a K–M binary system. Analysis of its spectra and rotation period reveal the star to be young, with an age of 200₋₂₀₀⁺⁴⁰⁰ Myr. TOI-8l5b has a 11.2-day period and a radius of 2.94 ± 0.05 R_⊕ with transits observed by TESS, CHEOPS, ASTEP, and LCOGT. The outer planet, TOI-8l5c, has a radius of 2.62 ± 0.10 R_⊕, based on observations of three nonconsecutive transits with TESS; targeted CHEOPS photometry and radial velocity follow-up with ESPRESSO were required to confirm the 35-day period. ESPRESSO confirmed the planetary nature of both planets and measured masses of 7.6 ± 1.5 M_⊕ (ρ_P = 1.64_−0.31^+0.33 g cm⁻³) and 23.5 ± 2.4 M_⊕ (ρ_P = 7.2_−1.0^+1.1 g cm⁻³), respectively. Thus, the planets have very different masses, which is unusual for compact multi-planet systems. Moreover, our statistical analysis of mini-Neptunes orbiting FGK stars suggests that weakly irradiated planets tend to have higher bulk densities compared to those undergoing strong irradiation. This could be ascribed to their cooler atmospheres, which are more compressed and denser. Internal structure modeling of TOI-815b suggests it likely has a H-He atmosphere that constitutes a few percent of the total planet mass, or higher if the planet is assumed to have no water. In contrast, the measured mass and radius of TOI-815c can be explained without invoking any atmosphere, challenging planetary formation theories. Finally, we infer from our measurements that the star is viewed close to pole-on, which implies a spin-orbit misalignment at the 3σ level. This emphasizes the peculiarity of the system’s orbital architecture, and probably hints at an eventful dynamical history.