  We derive a global higher regularity result for weak solutions of the linear
relaxed micromorphic model on smooth domains. The governing equations consist
of a linear elliptic system of partial differential equations that is coupled
with a system of Maxwell-type. The result is obtained by combining a Helmholtz
decomposition argument with regularity results for linear elliptic systems and
the classical embedding of $H(\mathrm{div};\Omega)\cap
H_0(\mathrm{curl};\Omega)$ into $H^1(\Omega)$.
