Foams have been widely studied across various disciplines, including biomedicine, cosmetics, food, agriculture, and construction. Although foams are extensively used, many of them rely on petroleum-based polymers, thereby contributing to environmental pollution. However, foams exhibit remarkable mechanical properties, such as thermal and physical resistance, and they can be manufactured using polysaccharides or proteins. For example, sodium alginate, a linear anionic polysaccharide composed of α-L-glucuronic acid and β-D-mannuronic acid, and water-soluble vegetable proteins can be used to form emulsions and foams. This study aimed to develop and characterize the stability of a polymeric foam based on chickpea protein and sodium alginate for potential use in biodegradable packaging materials. To prepare the foams, a 2.5% sodium alginate solution, aquafaba (chickpea cooking water), and an equimolar solution of calcium chloride–sodium citrate as a chelating agent were used. Various ratios of alginate to protein (1:1, 1:0.5, 1:5, and 1:0) were tested, and the pH was adjusted to optimize the foam's stability and mechanical properties. Micrographs were taken every 30 min to evaluate air loss and bubble size. The results showed that foams could not be obtained using alginate alone, and excess protein led to excessive air incorporation and poor gelation. Decreasing the protein content improved the texture but reduced the amount of entrapped air. The most stable foams with a homogeneous bubble size were achieved at a 1:1 alginate-to-protein ratio and a pH between 5.5 and 6.5. The foam's stability improved with a reduction in pH, and its firmness increased between a pH of 5.5 and 6.5. Additional optimization of the formulation by varying the speed, time, and alginate–calcium ratio is necessary. This study demonstrates the potential of protein–alginate foams as an environmentally friendly option for packaging materials and other industries.