Using non-archimedean q-integrals on defined in [T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory 76 (1999) 320–329; T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002) 288–299], we define new Changhee q-Euler polynomials and numbers which are different from those of Kim [T. Kim, p-adic q-integrals associated with the Changhee–Barnes’ q-Bernoulli polynomials, Integral Transforms Spec. Funct. 15 (2004) 415–420] and Carlitz [L. Carlitz, q-Bernoulli and Eulerian numbers, Trans. Amer. Math. Soc. 76 (1954) 332–350]. We define generating functions of multiple q-Euler numbers and polynomials. Furthermore we construct a multivariate Hurwitz type zeta function which interpolates the multivariate q-Euler numbers or polynomials at negative integers.