With the usage of two transparent electrodes, organic solar cells are semitransparent and may be combined to parallel-connected multi-junction devices or used for innovative applications like power-generating windows. A challenging issue is the optimization of the electrodes, in order to combine high transparency with adequate electric properties. In the present work, we study the potential of sputter-deposited aluminum-doped zinc oxide (AZO) as an alternative to the widely used but relatively expensive indium tin oxide (ITO) as cathode material in semitransparent polymer-fullerene solar cells. Concerning the anode, we utilized an insulator/metal/insulator structure based on ultra-thin Au films embedded between two evaporated MoO$_3$ layers, with the outer MoO$_3$ film (capping layer) serving as a light coupling layer. The performance of the ITO-free semitransparent solar cells is systematically studied as dependent on the thickness of the capping layer and the active layer, as well as the illumination direction. These variations are found to have strong impact on the obtained photocurrent. We performed optical simulations of the electric field distribution within the devices to analyze the origin of the current variations and provide deep insight in the device physics. With the conventional absorber materials studied herein, optimized ITO-free and semitransparent devices reached 2.0% power conversion efficiency and a maximum optical transmission of 60%, with the device concept being potentially transferable to other absorber materials.