Cross-sectional and plane-view transmission electron microscopy (X- and PV-TEM) were used to investigate the initial growth phase of 5-, 10-, 20- and 40-nm-thick Ni0.30Fe0.70 films, which were prepared on MgO(001), MgO(110), MgO(111) and on MgO(001) covered with a buffer layer. The 10-nm-thick BCC-Fe buffer layers and the 1.7- or 5.1-nm-thick Permalloy (FCC-Ni0.70Fe0.30) buffer layers were pre-grown on MgO(001). All of Ni0.30Fe0.70, Fe and Permalloy films were prepared at the optimum epitaxial growth condition by de-biased plasma sputtering at 2.9 kV in pure Ar gas. Saturation magnetization and coercive force of some samples were measured at r.t. using a vibration sample magnetometer (VSM). The Ni0.30Fe0.70 films were grown in the BCC phase with Ni-Fe(001)[110]//MgO(001)[100] up to 5 nm thickness on MgO(001) while up to 10 nm on Fe/MgO(001). With increasing thickness, the growth phase transformed into the stable Invar phase, i.e. into the FCC phase with Ni-Fe(001)[100]//MgO(001)[100]. The Ni0.30Fe0.70 FCC phase was grown from the initial growth stage on MgO(110), MgO(111) as well as on Pemalloy/MgO(001) substrates. Whether or not the Ni0.30Fe0.70 film can initially grow in the BCC phase depends primarily on the lattice misfit between the crystal planes in contact. The transformation of the growth phase from BCC to FCC was also confirmed by the thickness dependence of magnetic properties. Finally, the stability of initial growth structures for the present sample systems was simulated in terms of the lattice misfit between adjoining lattice planes.