In this paper we develop two approaches for studying a large family of generalized Bernoulli-Euler polynomials. For the determinental approach, using Little Fermat's Theorem, we establish a congruence identity and we give an explicit formulas of the generalized Bernoulli-Euler polynomials in terms of the Stirling numbers. The linear recursive approach allows us to formulate some properties of the generalized Bernoulli-Euler numbers and the generalized Bernoulli-Euler polynomials. Moreover, combinatorial formulas for these polynomials are provided.