This study aimed at demonstrating the usefulness and flexibility of the Bayesian structural equation modeling approximate measurement invariance (BSEM-AMI) approach to within-couple data. The substantive aim of the study was investigating partner differences in the perception of relationship quality (RQ) in a sample of intact couples (n = 435) drawn from the first sweep of the Millenium Cohort Study. Configural, weak and strong invariance models were tested using both maximum likelihood (ML) and BSEM approaches. As evidence of a lack of strong invariance was found, full and partial AMI models were specified, allowing nine different prior variances or "wiggle rooms." Although we could find an adequately fitting BSEM-AMI model allowing for approximate invariance of all the intercepts, the two-step approach proposed by Muthén and Asparouhov (2013b) for identifying problematic parameters and applying AMI only to them provided less biased results. Findings similar to the ML partial invariance model, led us to conclude that women reported a higher RQ than men. The results of this study highlight the need to inspect parameterization indeterminacy (or alignment) and support the efficacy of the two-step approach to BSEM-AMI.