Organizations have experienced a significant dependence on their Information and Communication Technology (ICT) infrastructure. To manage this infrastructure, they should follow several standards and good practices, which makes this task a challenge. In this paper, we propose the framework GAIA Infrastructure, that aims to support the ICT infrastructure management under different perspectives such as configuration, structured cabling, fault identification and mitigation and information security. The framework is composed by a Diagnostic Assessment Questionnaire, a Maturity Model and seven Assessment Axes. The framework was applied in three organizations and, therefore, they could identify strong and weak points of their infrastructure management practices.