Multiple instances of the_time

I’m trying to find a way to separate the day and month so I can style them separately. However, when I publish two posts on the same day, the last post loses it’s day but not month. Here is the code I am currently using.

<time class="updated">
    <span class="day"><?php the_time('d'); ?></span>
    <span class="month"><?php the_time('m'); ?></span>
</time>

I’ve tried mixing and matching different things like the_date or get_the_date but I still run into the same issue. Any help would be great. Thanks!