Emulsion-based edible films made of soy protein isolate (SPI), virgin coconut oil (VCO), and soy lecithin (SL) and plasticized with glycerol were prepared using the casting method. The effect of VCO and SL concentrations in SPI films and their in-between interaction were studied through the evaluation of physical (moisture and opacity), mechanical (elongation and tensile strength), water vapor permeability, and thermal properties. The response surface methodology was used to identify the most significant factors in the properties studied. The applicability of SPI emulsion-based films was evaluated as a package for olive oil to be used in small portions. The oxidative stability of the packaged olive oil was monitored by peroxide analyses during 28 days. The incorporation of VCO and SL decreased the moisture content and increased the elongation of the SPI emulsion-based films when compared to the SPI film without these components (control). The opacity of the films increased with the addition of VCO into the protein-based films, but not with the addition of SL or a combination of both constituents. By the other hand, the water vapor permeability was not improved by the incorporation of VCO, SL, or a combination of both. The peroxide value of the olive oil stored in SPI emulsion-based film sachets increased rapidly during the seven first days of storage. After this period, the peroxides increased relatively slow up to 28 days of storage. The peroxide values of the packaged olive oil did not reach the maximum limit recommended by the Codex Alimentarius. Based on these results, this work may be useful for the technological enhancement of emulsion-based films or for food packaging applications.