Multiple password forms + password completion

On the website I am working on we have a login and a private login, the problem I am having is that Firefox cannot seem to distinguish between these login forms.

Does anyone know how I can clarify that these are different logins?

I've already tried to give form fields different names and IDs like: onsite_login and login, but with no success.

edit: my form tags don't mix, they aren't even on the same page

Two forms on different pages

<form method="post" action="/en/login/1">
<fieldset>
    <p>
        <input type="hidden" value="login" name="form"/>
        <input type="hidden" value="en" name="redirect"/>
        <label for="onsite_username">Username<abbr title="Required ">*</abbr></label>
        <input type="text" class="input-text" maxlength="255" value="" name="onsite_username" id="onsite_username"/>
        <label for="onsite_password">Password<abbr title="Required ">*</abbr></label>
        <input type="password" class="input-password" maxlength="255" value="" name="onsite_password" id="onsite_password"/>
        <input type="submit" value="Log in" name="submit" class="input-submit"/>
    </p>
</fieldset>
</form>

      

        
        
        
      

    

and

<form method="post" action="">
<fieldset>
    <input type="hidden" value="login" name="form"/>
    <div>
        <label for="username">Username</label>
        <input type="text" class="input-text" value="" name="username" id="username"/>
    </div><div>
        <label for="password">Password</label>
        <input type="password" class="input-password" value="" name="password" id="password"/>
    </div>
    <input type="submit" value="Aanmelden" class="input-submit"/>
</fieldset>
</form>