Passive permeation through lipid membranes is an essential process in biology. In vivo membranes typically consist of mixtures of lamellar and nonlamellar lipids. Lamellar lipids are characterized by their tendency to form lamellar sheet-like structures, which are predominant in nature. Nonlamellar lipids, when isolated, instead form more geometrically complex nonlamellar phases. While mixed lamellar/nonlamellar lipid membranes tend to adopt the ubiquitous lamellar bilayer structure, the presence of nonlamellar lipids is known to have profound effects on key membrane properties, such as internal distributions of stress and elastic properties, which in turn may alter related biological processes. This work focuses on one such process, i.e., permeation, by utilising atomistic molecular dynamics simulations in order to obtain transfer free energy profiles, diffusion profiles and permeation coefficients for a series of thirteen small molecules and drugs. Each permeant is tested on two bilayer membranes of different lipid composition, i.e., purely lamellar and mixed lamellar/nonlamellar. Our results indicate that the presence of nonlamellar lipids reduces permeation for smaller molecules (molecular weight < 100) but facilitates it for the largest ones (molecular weight > 100). This work represents an advancement towards the development of more realistic in silico permeability assays, which may have a substantial future impact in the area of rational drug design.