There is nothing wrong, as far as Islam is concerned, in making a double intention by fasting the missed day(s) of obligatory fasting in Ramadan while fasting on the 10th and the 11th of Muharram.
The Saudi House of Fatwa issued the following fatwa on the issue:
First, it is better not to observe voluntary fasts when you still owe one or more days from Ramadan. Rather you should start with the fasts that you owe from Ramadan, and then observe voluntary fasts.
Second, if you fast the 10th and 11th of Muharram with the intention of making up for days that you owe from Ramadan, then it is permissible and will make up for two of the days that you owe. The Prophet (peace and blessings be upon him) is reported to have said, “Actions are judged but by intentions, and everyone shall have but that which he intended.” (Bukhari and Muslim)
We hope that you will have the reward for making up the missed fast and the reward for fasting that day.