We consider the time-harmonic Maxwell equations set on a domain made of a magnetic conductor subdomain and a dielectric in a regime where the relative magnetic permeability $\mu_{r}$ between the subdomains is large. 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 electric 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 admits a multiscale expansion in powers of $\varepsilon=1/\sqrt{\mu_{r}}$ 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 $\varepsilon$ tends to zero. We derive also impedance boundary conditions (IBCs) on the interface up to the third order of approximation with respect to $\varepsilon$.