The answer is yes, but there are good reasons to hold off on the car loan until you have closed on the home loan, if you can.
The reason to not apply for both at the same time is that lenders can see you are taking on significant new debt in two places. This means lenders are likely to evaluate you as a higher risk. This can result in less favorable rates on both loans, and if your credit history is not exceptional, you may even be denied one or both loans.
Your best bet is to apply for the home loan first. You’re borrowing much more money for a longer time, so it’s important to qualify for the lowest rate and best terms on that loan. Once the home loan is approved and closed, then apply for the car loan. Even if the rate is a bit higher (because you now have a mortgage), it will likely be better than if you had been approved for the car loan at the same time as the mortgage.