Could not find a base address that matches scheme http for the endpoint with binding WebHttpBinding. Registered base address schemes are [https]
So apparently my WCF service registered itself as HTTPS (since it is over SSL), but my binding was only configured for HTTP. The solution is to define a custom binding inside your Web.Config file and set the security mode to "Transport". Then you just need to use the bindingConfiguration property inside your endpoint definition to point to your custom binding. The entire HTTPS-enabled system.serviceModel section is below:
<serviceHostingEnvironment aspNetCompatibilityEnabled="true" />
<endpoint address="" behaviorConfiguration="TestServiceAspNetAjaxBehavior"
binding="webHttpBinding" bindingConfiguration="webBinding" contract="TestService" />
Hopefully this will help someone who has the same problem.