A new procedure for solving coupled ordinary and partial differential equations systems containing multiple internal interfaces is proposed in this paper. The method has interest in systems that may be encountered in electrochemical problems, more specifically in batteries whose inner regions are composed by liquid and solid juxtaposed subdomains. However, the method application is general. The central contribution of the procedure is a QR factorization algorithm based on modified Householder transformations for block systems. Its application performance is demonstrated with a numerical example, where despite the more ellaborate mathematical algorithm less refined mesh discretizations are necessary for accurate solutions. (C) 2016 The Electrochemical Society. All rights reserved.