I achieved webpublish with these information :
$websiteName = "mywebsite"
#Get the website's propeties.
$website = Get-AzureWebSite -Name $webSiteName
$siteProperties = $website.SiteProperties.Properties
#extract url, username and password
$url = ($siteProperties | ?{ $_.Name -eq "RepositoryURI" }).Value.ToString() + "/MsDeploy.axd"
$userName = ($siteProperties | ?{ $_.Name -eq "PublishingUsername" }).Value
$pw = ($siteProperties | ?{ $_.Name -eq "PublishingPassword" }).Value
#build the command line argument for the deploy.cmd :
$argFormat = ' /y /m:"{0}" -allowUntrusted /u:"{1}" /p:"{2}" /a:Basic "-setParam:name=DeployIisAppPath,value={3}"'
$arguments = [string]::Format($argFormat, $url, $userName, $pw, $webSiteName)
I then use this line to call the cmd script generated with the publish package.