Multi-layer bags may be formed to include first and second sidewalls joined along a first side edge, an opposite second side edge, and a closed bottom edge. The first and second layers may be non-continuously laminated together to include bonded regions in which the layers are bonded and unbonded regions in which the layers are not bonded. Such a bag may be described as a “bag-in-a-bag” type configuration in which the inner bag is non-continuously bonded to the outer bag. The inventors have surprisingly found that such configurations of non-continuous bonding provides increased and unexpected strength properties to the multi-layer films and bags.