Microwave cooking packages suitable for use as microwave popcorn packages include at least one panel (e.g., first and second panels) formed of a vertically rigid material. A flexible portion is attached to the panels. The flexible portion may be formed of a polyester film material such as a biaxially-oriented polyethylene terephthalate (PET) film, which may be at least partially transparent. The flexible portion (and panels) defines a bag construction configured to contain a popcorn charge and to be expandable between a collapsed configuration and an expanded configuration when the popcorn charge is subjected to a popping operation. The microwave cooking package may include a vent assembly configured to at least partially open when the bag configuration is in an expanded configuration to vent the bag construction. The vent assembly includes a first portion a second portion of the bag construction that is configured to be folded against the first portion.