We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., g(x)=(eax+e−bx)−1, Rea,Reb>0. A criterion for half-regular sampling is obtained: for a separated Λ⊂R the Gabor system G(g,Λ×αZ) is a frame in L2(R) if and only if D−(Λ)>α where D−(Λ) is the usual (Beurling) lower density of Λ. This extends a result by Gröchenig, Romero, and Stöckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by g is given. © 2024 Elsevier Inc.