Yes, it is now possible with the latest Azure platform updates that were released late 2010.
You have to make the appropriate config changes in your Azure Project's service definition file. Below is an example of multiple sites on the same domain. The Register site is using an https endpoint (you must also configure your cert) and the rest are using http. The Public site does not specify a host header and will catch anything not explicity specified. This is great when you have one app that needs to handle multiple subdomains (like shopify). In order to make this work you need to have a dns that allows wildcard cnames (GoDaddy dns does not). Obviously, you also need a cname record that points to azure for each of the other subdomains. One other thing to note in this example is that the physicalDirectory for the apps are relative to the Azure Project. Hope this helps!
Here's a link that may help: http://msdn.microsoft.com/en-us/library/gg433110.aspx
<?xml version="1.0" encoding="utf-8"?>
<ServiceDefinition name="SampleAzureProject" xmlns="http://schemas.microsoft.com/ServiceHosting/2008/10/ServiceDefinition">
<WebRole name="RegisterSite_WebRole">
<Sites>
<Site name="RegisterSite" physicalDirectory="..RegisterSite">
<Bindings>
<Binding name="RegisterBinding" endpointName="Endpoint1" hostHeader="register.sample.com" />
</Bindings>
</Site>
<Site name="PublicSite" physicalDirectory="..PublicSite">
<Bindings>
<Binding name="PublicBinding" endpointName="Endpoint2" hostHeader="" />
</Bindings>
</Site>
<Site name="ManageSite" physicalDirectory="..ManageSite">
<Bindings>
<Binding name="ManageBinding" endpointName="Endpoint2" hostHeader="manage.sample.com" />
</Bindings>
</Site>
<Site name="MarketingSite" physicalDirectory="..MarketingSite">
<Bindings>
<Binding name="MarketingBinding" endpointName="Endpoint2" hostHeader="www.sample.com" />
</Bindings>
</Site>
</Sites>
<Endpoints>
<InputEndpoint name="Endpoint1" protocol="https" port="443" certificate="SampleReg" />
<InputEndpoint name="Endpoint2" protocol="http" port="80" />
</Endpoints>
<Imports>
<Import moduleName="Diagnostics" />
</Imports>
<Certificates>
<Certificate name="SampleReg" storeLocation="LocalMachine" storeName="My" />
</Certificates>
</WebRole>
</ServiceDefinition>
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