We propose a novel joint sampling design for surveys involving two interrelated populations of parents and children in the presence of complex family structures, including shared parental responsibility and blended families. The design combines a graph-theoretic representation of co-parenting relationships with balanced sampling. This framework ensures that, in the first sampling phase, exactly one parent is selected from each co-responsibility pair while maintaining accurate inference for both the parent and child populations. A second sampling phase selects one child per sampled parent using unequal probabilities that produce consistent weighting and unbiased estimation. The proposed framework accommodates overlapping family relationships while balancing auxiliary information for both populations. Results based on the Luxembourg population registers show that the estimated totals are virtually identical to the known population totals for all balancing variables, and other auxiliary variables, demonstrating the excellent precision and efficiency of the proposed sampling design.

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