The short answer is yes. And no.
This comes down completely to style and personal opinion—and what one person believes may be completely different from what another person believes.
Even the two most common style guides in North America give different guidance.
According to The Chicago Manual of Style (17th ed.), 7.53:
Use italics for isolated words and phrases from another language unless they appear in Webster’s or another standard English-language dictionary.
And, from an example, the English translation is in parentheses in roman type:
The word he used, Kaffeetasse (coffee cup), was just accurate enough to gain the desired result.
But according to the Associated Press Stylebook:
AP does not italicize words in news stories. Italics are used in Stylebook entries to highlight examples of correct and incorrect usage.
I have a book review that refers to Castro as El Presidente. Would AP cap that term? And, since we use italics to indicate foreign words that are italicized in Webster's, would this get italicized?
from Farmington, Maine on March 08, 2013
AP Spanish language stories lowercase el presidente preceding a name. Your call on italics. AP doesn't use italics in news stories.
Also this, which is related to the translation:
When quoting a text message, how should the spelling and capitalization be rendered? As it was sent? (Her last text to him was "cu l8ter.") In normal English? (Her last text to him was "See you later.") Or a combination? (Her last text to him was "cu l8ter," shorthand for "see you later.")
from New York, NY on July 09, 2009
We don't see many of these yet. But I like the last solution with a translation.
Based purely on those style guide entries, the phrase might appear styled in one of two ways.
in medias res (in the middle)
"In medias res," Latin for "in the middle."
But italics aside (which is treated different by each guide), neither guide gives specific guidance on how to present or style the English translation that follows the Latin—they simply give an example, which may or may not be taken as authoritative according to them.
This also doesn't mention the fact that your company name is presented in lowercase rather than in title caps (which would make it In Medias Res, either in italics or roman text).
In your case, you're not even talking about narrative text (as would Chicago mainly refer to) or news stories (as would covered by AP). Instead, you're talking about business cards. I don't know of any style guide that covers business cards specifically.
In short, there is no answer that can be given here that really helps you decide what you should be doing for your own company's business cards.
For what it's worth, here is my personal opinion: have it match whatever is on your letterhead and other correspondence.
I'm assuming that you're using in media res rather than In Media Res because your company already decided to use lowercase for the company name. Since you're using the same capitalization on the business cards as is used elsewhere, I would maintain consistency when it comes to the type on your business cards.
If the name of the company is in roman type on your letterhead, then keep it in roman type on your business cards. I think it would be strange to have it styled differently from one medium to the next.
Similarly, and for the same reasoning, if the translation of the phrase doesn't appear on your letterhead, then don't have appear on your business cards.
However, that's far from any kind of authoritative statement. I've seen many companies put things on their business cards that aren't used elsewhere. So, if a translation makes sense in your case, you should provide one. I just can't say how you should style it.
Perhaps at the very least, a business card it should be catchy. So, everything else being equal, if a particular style isn't catchy, it's probably not a style you should use.