The structure of the thermoelectric lamellar misfit cobalt oxide [Bi0.84CaO2]2[CoO2]1.69 has been refined using single crystal X-ray diffraction data. Using the four dimensional superspace formalism for aperiodic structures, the superspace group is confirmed P2/m(0delta1/2) (a1 = 4.9069(4), b1 = 4.7135(7), b2 = 2.8256(4), c1 = 14.668(5) A, beta1 = 93.32(1) degrees). The modulated displacements and site occupancies have been refined and are both compatible with the misfit character of the structure, and with a longitudinal modulation of the Bi-O layers of the structure. This modulation is similar to the corresponding one in the related Sr phase [Bi0.87SrO2]2[CoO2]1.82, but now oriented in the orthogonal direction. Because its incommensurate wavelength is locked with the aperiodicity of the misfit structure, it is possible to distinguish between the modulation parameters induced by the accommodation of both subsystems and those related to the longitudinal modulation of the Bi-O layers. In this original structure, two independent aperiodic phenomena coexist in an single crystallographic direction. A particular attention has been paid to the structural configuration of the CoO2 layer, in relation with other similar phases. The thermoelectric properties are probably directly related to the specific distortion of the compressed layer, but the different measured values for the Seebeck coefficient cannot be related to a significant modification of the CoO6 octahedra.