Andreev reflection (AR) in ferromagnet/superconductor junctions is an indispensable spectroscopic tool for measuring spin polarization. We study theoretically how the presence of a thin semiconducting interface in such junctions, inducing Rashba and Dresselhaus spin-orbit coupling, modifies AR processes. The interface gives rise to a momentum-and spin-dependent scattering potential, making the AR probability strongly asymmetric with respect to the sign of the incident electrons' transverse momenta. This skew AR creates spatial charge carrier imbalances and transverse Hall currents in the ferromagnet. We show that the effect is giant, compared to the normal regime. We provide a quantitative analysis and a qualitative picture of this phenomenon, and finally show that skew AR also leads to a widely tunable transverse supercurrent response in the superconductor. strate that, analogously to the tunneling picture in the normalconducting case, skew reflection [49] of spin-polarized carriers at the barrier leads to TAHEs in the F. Due to the presence of a S electrode, we distinguish two skew reflection processes: skew specular reflection (SR) and skew Andreev reflection (AR). By formulating a qualitative physical picture including both processes, we assert that skew SR and skew AR can act together and significantly enhance the TAHE compared to all previously studied (normal) systems. Special attention must be paid to skew AR, which transfers Cooper pairs across the barrier into the S. The electrons forming one Cooper pair are thereby also subject to the proposed skew reflection mechanism. We discuss that the result is a transverse supercurrent response, initially deduced from a phenomenological Ginzburg-Landau treatment [50], with widely tunable characteristics. Both findings, relatively giant TAHE conductances in the F and transverse supercurrents in the S, are distinct fingerprints to experimentally detect skew AR and characterize the junctions' interfacial SOC.We consider a biased ballistic F/SC/S junction grown along theẑ-direction, in which the two semi-infinite F and S regions are separated by an ultrathin SC barrier [see Fig. 1(a)]. The barrier may be composed of a thin layer of zincblende materials (e.g., GaAs or InAs) and introduces potential scattering, as well as strong interfacial Rashba [16] and Dresselhaus [17] SOC [18,19].The system can be modeled by means of the stationary Bogoljubov-de Gennes (BdG) Hamiltonian [51],SCσ0 δ(z)+Ĥ SOC SC δ(z) represents the single-electron Hamiltonian andĤ h = −σ yĤ * eσy its holelike counterpart (σ 0 andσ i indicate the 2 × 2 identity and the ith Pauli matrix; σ = [σ x ,σ y ,σ z ] is the vector of Pauli matrices). The F is described within the Stoner model with exchange energy ∆ XC and magnetization directionm = [cos Φ, sin Φ, 0] , where Φ is measured with respect to thex-axis. Following earlier studies [52-56], the ultrathin SC layer is included into our model as a δ-like barrier with height V SC and width d SC ; its SOC enters the Hamiltonian [18, 19]Ĥ SOC SC = α (k yσx ...