This paper introduces a bi-anisotropic frequency selective surface (BFSS) that provides absorption from one illuminating side, and partial reflections (PR) from the other illuminating side, along with non-zero in-band (IB) and out-of-band (OB) transmissions. When an x-polarized or y-polarized wave is incident on the front side of the BFSS, over 90% of the incident waves are absorbed in the frequency band of 13.1–13.6 GHz. Similarly, when the back side of the BFSS is excited with an x-polarized or y-polarized incident wave, almost 85% of the incident wave is reflected (PR) in the frequency band of 13.1–13.6 GHz. Moreover, due to the absence of a complete ground plane, in-band (IB) and out-of-band (OB) transmissions are achieved in the frequency bands of 13.1–13.6 and 11.1 GHz to 12.3 GHz, respectively. The proposed structure behaves the same against the oblique incident angle up to 60°. Besides, the BFSS response remains consistent against any arbitrary oriented linearly polarized wave or circularly polarized incident wave. The proposed BFSS with simultaneous absorption, PR, IB transmission, OB transmission, polarization insensitivity, and angular stability is a vital candidate for various microwave applications.