Upvote:3
This is fairly common actually and in fact is often the only way allowed. Generally, citizens of a country are not allowed to apply for a visa to their own country. Although can apply as a citizen of the other country, visa forms tend to ask a lot of question covering your background, including whether you are a citizen of another country. Plus, it is common for countries to specify that citizens of their own country must use the matching passport when entering or exiting.
The typical procedure is to show passports as follow when going from your origin to your destination:
And as follows when returning from your destination to the origin:
Given all possible combination of countries, it is likely that there are some exceptions to the above procedure but that would require a more specific question. Also, it is possible to encounter some complications such as when your travel documents have different names and one way or the other, the name on the passport does not match the ticket on the name. For small differences (such as accented characters missing accents on one or a truncated name), they will often be understood but more significant differences will be an issue.