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The coexisting regime of spin-density wave (SDW) and superconductivity in iron pnictides represents a novel ground state. We have performed high-resolution angle-resolved photoemission measurements on NaFe_{1-x}Co_{x}As (x=0.0175) in this regime and revealed its distinctive electronic structure, which provides some microscopic understandings of its behavior. The SDW signature and the superconducting gap are observed on the same bands, illustrating the intrinsic nature of the coexistence. However, because the SDW and superconductivity are manifested in different parts of the band structure, their competition is nonexclusive. Particularly, we find that the gap distribution is anisotropic and nodeless, in contrast to the isotropic superconducting gap observed in a SDW-free NaFe_{1-x}Co_{x}As (x=0.045), which puts strong constraints on theory.