If you lose your job and primary health insurance but are also covered through your spouse's group plan are you still eligible for COBRA?

That would depend on if your spouse's coverage is group or individual coverage. If it is group coverage offered by your spouse's employer then NO. Cobra regulations specifically say that you are not eligible if you have other employer sponsored group coverage with one exception. That is if the other coverage includes any pre-exisitng conditions clause that would deny you coverage for that illness/injury. If you have no pre-existing conditions or the pre-ex caluse does not relate to you (ie. pregnancy is a pre-ex but you are not pregnant) then you are not eligible.
If the spouse's coverage is individual coverage and not group you are still eligible for Cobra.