We consider the time-harmonic Maxwell equations set on a domain which represents a magnetic conductor surrounded by an insulating body such that the relative magnetic permeability between the materials is very high. We prove uniform a priori estimates for Maxwell transmission problem when the interface between the two subdomains is supposed to be Lipschitz. The technique is based on an appropriate decomposition of the magnetic field, whose gradient part is estimated thanks to uniform estimates for a scalar transmission problems with constant coefficients on two subdomains. Assuming smoothness for the interface between the subdomains, we prove that the solution of the Maxwell equations possesses a multiscale expansion in powers of a small parameter ε (which is the inverse of the square root of the relative permeability) with profile terms rapidly decaying inside the magnetic conductor. As an application of uniform estimates, we develop an argument for the convergence of this expansion as ε tends to zero. We derive also impedance boundary conditions on the interface up to the third order of approximation with respect to ε.