We assessed if immune responses are enhanced in CD-1 mice by heterologous vaccination with two different nucleic acid-based COVID-19 vaccines: a next-generation human adenovirus serotype 5 (hAd5)-vectored dual-antigen spike (S) and nucleocapsid (N) vaccine (AdS+N) and a self-amplifying and -adjuvanted S RNA vaccine (AAHI-SC2) delivered by a nanostructured lipid carrier. The AdS+N vaccine encodes S modified with a fusion motif to increase cell-surface expression and an N antigen modified with an Enhanced T-cell Stimulation Domain (N-ETSD) to direct N to the endosomal/lysosomal compartment and increase MHC class I and II stimulation potential. The S sequence in the AAHI-SC2 vaccine comprises the D614G mutation, two prolines to stabilize S in the prefusion conformation, and 3 glutamines in the furin cleavage region to confer protease resistance. CD-1 mice received vaccination by homologous and heterologous prime > boost combinations. Humoral responses to S were the highest with any regimen that included the AAHI-SC2 vaccine, and IgG bound to wild type and Delta (B.1.617.2) variant S1 at similar levels. An AAHI-SC2 prime followed by an AdS+N boost particularly enhanced CD4+ and CD8+ T-cell responses to both wild type and Delta S peptides relative to all other vaccine regimens. Sera from mice receiving AAHI-SC2 homologous or heterologous vaccination were found to be highly neutralizing for all pseudovirus strains tested: Wuhan, Beta, Delta, and Omicron strains. The findings here, taken in consideration with the availability of both vaccines in thermostable formulations, support the testing of heterologous vaccination by an AAHI-SC2 > AdS+N regimen in animal models of SARS-CoV-2 infection to assess its potential to provide increased protection against emerging SARS-CoV-2 variants particularly in regions of the world where the need for cold-chain storage has limited the distribution of other vaccines.