A Neutron Powder Diffraction (NPD) experiment has been performed to investigate the structural phase transition and magnetic order in CaFe1-xCoxAsF superconductor compounds (x = 0, 0.06, 0.12). The parent compound CaFeAsF undergoes a tetragonal to orthorhombic phase transition at 134(3) K, while the magnetic order in form of a spin-density wave (SDW) sets in at 114(3) K. The antiferromagnetic structure of the parent compound has been determined with a unique propagation vector k = (1,0,1) and the Fe saturation moment of 0.49(5)uB aligned along the long a-axis. With increasing Co doping, the long range antiferromagnetic order has been observed to coexist with superconductivity in the orthorhombic phase of the underdoped CaFe0.94Co0.06AsF with a reduced Fe moment (0.15(5)uB). Magnetic order is completely suppressed in optimally doped CaFe0.88Co0.12AsF. We argue that the coexistence of SDW and superconductivity might be related to mesoscopic phase separation.