We present a systematic investigation of the electrical, structural, and antiferromagnetic properties for the series of Ba(Fe1 −x−yCoxRhy)2As2 compounds with fixed x ≈ 0.027 and 0 ≤ y ≤ 0.035. We compare our results for the Co-Rh doped Ba(Fe1−x−yCoxRhy)2As2 compounds with the Co doped Ba(Fe1−xCox)2As2 compounds. We demonstrate that the electrical, structural, antiferromagnetic, and superconducting properties of the Co-Rh doped compounds are similar to the properties of the Co doped compounds. We find that the overall behaviors of Ba(Fe1−x−yCoxRhy)2As2 and Ba(Fe1−xCox)2As2 compounds are very similar when the total number of extra electrons per Fe/TM (TM=transition metal) site is considered, which is consistent with the rigid band model. Despite the similarity, we find that the details of the transitions, for example, the temperature difference between the structural and antiferromagnetic transition temperatures and the incommensurability of the antiferromangetic peaks, are different between Ba(Fe1−x−yCoxRhy)2As2 and Ba(Fe1−xCox)2As2 compounds.