Most likely the font you have chosen doesn't have the correct glyphs included for the Hungarian text and you'll need to find a diferent font with the correct language support.
Try Minion Pro.
The Minion Pro works... I wish there was another solution so that the company font can be kept but I did it this way
If you are missing only one character in your company identity font, you can use the IndyFont Demo to create a one-character font with just the missing character. You can use the company font as template.
You can use the original font for all regular text and use a GREP style to apply the custom font to just the missing character -- and you'll never miss it.
The IndyFont demo allows only one single character per font, and so it will even work if you need the same character in different styles. Create a separate font for Regular, Bold, Italic and Bold Italic, all with the same Font Name. If you only apply the font name in your GREP style and leave the "style" field blank, InDesign will automatically use whatever style the main text has.
See Indiscripts :: What's New in IndyFont 1.135 for a longer description, a manual, and the Demo Download link.