You can use windows azure powershell to upload/download huge files from azure.
Set-AzureStorageBlobContent is for uploading.
Set-AzureStorageBlobContent -Container containerName -File .\filename -Blob blobname
http://msdn.microsoft.com/en-us/library/dn408487.aspx
Get-AzureStorageBlobContent is for downloading.
Get-AzureStorageBlobContent -Container containername -Blob blob -Destination C:\test\
http://msdn.microsoft.com/en-us/library/dn408562.aspx