We show that foams and emulsions can display a fundamentally different normal response to a simple shear deformation. While foams dilate or push outwards on the shearing surfaces, known as a positive Poynting effect, in emulsions the Poynting effect can have either sign and can be tuned by changing the emulsion properties. We relate the sign of the Poynting effect to the presence of a compressible contact network supported by adhesive contacts. When the concentration of surfactant in the continuous phase is low, the emulsions are nonadhesive and push outward on their shearing surfaces, as do the foams. When the surfactant concentration is increased, the emulsions become adhesive due to depletion interactions, and the Poynting effect changes sign. We argue that the adhesive contact network develops a shear modulus that stiffens in response to dilation, which leads to the negative Poynting effect.