In roof-structure integrated aluminum alloy latticed shell structures, the flange of H-shaped members is equipped with convex ribs (referred to as “tongue”) to connect the roof panel with the members. The roof panel and flange tongue are connected by clamping the strip. The presence of the flange tongue and strip changes the cross-sectional characteristics of the member, affecting its mechanical properties. However, the influence of roof connection construction is often ignored in engineering design, and the members are only designed as biaxially symmetric H-shaped members. In this study, H-shaped aluminum members with roof-connection construction under two conditions, unsupported and effective lateral constraint, are subjected to compression tests to obtain the buckling mode and buckling strength. A numerical model of the members considering the roof-connection construction is proposed, and the influence of the presence or absence of constructions on the failure modes and buckling strength is investigated. Combined with experimental and finite element studies, the following conclusions are drawn. Regarding the failure modes, the presence of roof-connection constructions induces bending and additional twisting in freely buckling members. For members with lower slenderness ratios or larger plate thickness ratios, the construction exacerbates local buckling of the lower flange. Concerning buckling strength, the connection construction has an uplifting effect within the range of 10–20% for the unsupported members with large slenderness ratios. However, for the unsupported members with slenderness ratios and for those that are subjected to lateral constraints, the connection construction has a negative effect, with a minimum reduction of approximately 20%. The experimental and finite element results were further compared with those of the buckling calculation method under axial compression for biaxially symmetric H-bars in EC9, GB 50429, and AA, and the applicability of the calculation method was evaluated.