The K-user flat fading MIMO interference channel with J instantaneous relays (KICJR) is considered. In the KICJR, the effective channel between sources and destinations including the relays has certain structure and is non-generic. For non-generic channels, the achievable degrees of freedom (DoF) is still unknown. Lee and Wang showed that by using the aligned interference neutralization scheme 3/2 degrees of freedom is achievable in a 2IC1R system, which is 50% more than the 2-user interference channel. But the DoF performance and achievable schemes for other KICJR networks are not investigated in literature. In this paper we devise an achievable scheme called restricted interference alignment for instantaneous-relay aided interference channels. Also, to find insights to the maximum achievable degrees of freedom we develop linear beamforming based on the mean square error (MSE) minimization as an achievable scheme. Furthermore, we present upper-bounds on the maximum achievable degrees of freedom by investigating the properness of the interference alignment equation system. The numerical results show that the DoF performance of the proposed restricted interference alignment scheme and the MSE-based beamforming match the upper-bounds determined from the properness of the interference alignment equations.