The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar Pöschl-Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases. © World Scientific Publishing Company.