Dynamic contrast enhanced MRI (DCE-MRI) and dynamic susceptibility contrast MRI (DSC-MRI) are perfusion imaging techniques used mainly for clinical and preclinical measurement of vessel permeability and capillary blood flow, respectively. It is advantageous to apply both methods to exploit their complementary information about the perfusion status of the tissue. We propose a novel acquisition method that combines advantages of the current simultaneous and sequential acquisition. The proposed method consists of a DCE-MRI acquisition interrupted by DSC-MRI acquisition. A new method for processing of the DCE-MRI data is proposed which takes the interleaved acquisition into account. Analysis of both the DCE- and DSC-MRI data is reformulated so that they are approximated by the same pharmacokinetic model (constrained distributed capillary adiabatic tissue homogeneity model). This provides a straightforward evaluation of the methodology as some of the estimated DCE- and DSC-MRI perfusion parameters should be identical. Evaluation on synthetic data showed an acceptable precision and no apparent bias introduced by the interleaved character of the DCE-MRI acquisition. Intravascular perfusion parameters obtained from clinical glioma data showed a fairly high correlation of blood flow estimates from DCE- and DSC-MRI, however, an unknown scaling factor was still present mainly because of the tissue-specific relaxivity. The results show validity of the proposed acquisition method. They also indicate that simultaneous processing of both DCE- and DSC-MRI data with joint estimation of some perfusion parameters (included in both DCE- and DSC-MRI) might be possible to increase the reliability of the DCE- and DSC-MRI methods alone.