We investigate the magnetization dynamics through the magnetoimpedance effect in ferromagnetic NiFe/Cu/Co films. We observe that the magnetoimpedance response is dependent on the thickness of the non-magnetic Cu spacer material. We verify asymmetric magnetoimpedance in films with biphase magnetic behavior and explore the possibility of tuning the linear region of the magnetoimpedance curves around zero magnetic field by varying the thickness of the spacer and probe current frequency. We discuss the experimental results in terms of the different mechanisms governing the magnetization dynamics at distinct frequency ranges, quasi-static magnetic properties, thickness of the spacer, and the kind of the magnetic interaction between the ferromagnetic layers. The results place films with biphase magnetic behavior exhibiting asymmetric magnetoimpedance effect as very attractive candidates for application as probe element in the development of auto-biased linear magnetic field sensors.