One fact that emerges from the evaluation of the Millennium Development Goals is that not all countries met all the goals and there are significant complementaries among failing on specific goals. This paper proposes the Multidimensional Human Opportunity Index (MHOI) that focuses on the complementaries among access to multiple services. We focus on access to services for children, with the aim of capturing equality in opportunity for children from diverse socio-economic backgrounds. This index builds on the Human Opportunity Index of the World Bank that measures children’s access to a basic service, such as access to clean water. However, the MHOI differs from the parent index in that we measure joint access to multiple services or access to a bundle of services. We apply the MHOI on two Himalayan states of South Asia, Nepal and Bhutan, and show that although each basic service is available to a large proportion of the population, only two-thirds in Bhutan and one half in Nepal have access to the bundle of basic services in 2011–2012.