In this study, terebinth coffee formulations were prepared with whole or skimmed milk with or without sugar/sweetener in order to study the matrix effect on the bioaccessibility of terebinth polyphenols. Quercetin glycosides and catechin were the major flavonoids identified in the terebinth formulations, whereas gallic, protocatechuic, syringic and ellagic acids were determined as the non-flavonoid compounds. The in vitro gastrointestinal digestion model results revealed that addition of whole milk to terebinth coffee increased the total bioaccessible flavonoids significantly (45%) (p < 0.05), whereas skim milk addition did not result in any significant change. Furthermore, antioxidant capacity results measured with CUPRAC assay showed that addition of milk alone or together with sugar/sweetener increases the bioaccessibility of terebinth coffee antioxidants (36–70%) (p < 0.05). Overall, terebinth coffee + whole milk + sugar formulation was found to contain the highest amount of bioaccessible flavonoid and non-flavonoid compounds (42.71–47.07 mg/100 g).