A film that contains a core layer positioned adjacent to an outer layer is provided. The core layer contains a relatively high percentage of thermoplastic biopolymers that are both biodegradable and renewable. Despite being biodegradable and renewable, many biopolymers tend to be relatively stiff in nature. The present inventors have discovered, however, that through selective control over the components in the core and outer layers, a film can be readily formed having good mechanical properties. Among other things, this is accomplished by blending the biopolymer in the core layer with a polyolefin. A polyolefin is also employed in the outer layer. In addition to providing functionality to the film (e.g., heat sealing, printing, etc.), the polyolefin-containing outer layer also helps counteract the stiffness of the biopolymer in the core layer, and helps improve processability, stiffness, and ductility.