No, the difference is not just—or even primarily—one of duration. Although in any given environment /i:/ wil be longer than /ɪ/, their environments radically affect their durations. Because of this, the realisation of /i:/ in some environments will be shorter than that of /ɪ/ in others.
The difference between realisations of /i:/ and /ɪ/
Despite the fact that /i:/ for most speakers will be consistently and reliably longer than /ɪ/ in the same situation, this is not the most significant difference between the realisations of these two vowels. They are qualitatively different.
Just behind your teeth, you can feel it with your tongue, there is a little shelf that slopes slightly upwards. This is your alveolar ridge. Behind this, your mouth suddenly arches upwards to form the roof of your mouth. Now, if you feel just behind this ridge with your tongue you will be able to feel that this part of your mouth is hard and boney. This part of the roof of your mouth is your ʜᴀʀᴅ ᴘᴀʟᴀᴛᴇ. If you carry on exploring further backwards with the tip of your tongue (it gets a bit ticklish) you will feel that the roof of your mouth becomes soft and tissuey. This tissuey part of the roof of your mouth is your sᴏғᴛ ᴘᴀʟᴀᴛᴇ. This change happens about half way back.
When most speakers make an /i:/, that part of their tongue directly below where your hard and soft palate meet rises up very close to the roof of the mouth. If you are an RP (Southern Standard British English) speaker, it will come so close to the roof of your mouth that if it got much closer, it would cause the air passing through to become turbulent and would effectively turn the sound into a consonant. If you speak General American, then the gap between your tongue and the roof of your mouth will be ever so slightly bigger.
For most speakers, when they produce an /⁠ɪ/, the gap between their tongue and the roof of their mouths will be significantly bigger than it would be for /i:/. It will be nowhere near close enough to cause any turbulence. In addition that part of the tongue that will rise up towards the roof of the mouth will be some millimetres further back from that part that would rise up for /i:/.
The Original Poster's partner
It is important to realise that what I have described are typical realisations . So a given realisation of /i:/ might be varying degrees lower than IPA [i], and a realisation of /ɪ/ might be higher or lower or more front or more back than IPA [ɪ]. (I haven't talked at all about the diphthongalisation of /i:/, because I'm not sure it is helpful here)
The reason that the Original Poster (OP) can hear this difference in vowel quality, but their partner can't, is that in English this difference in vowel quality leads to a difference in meaning. So there are words in English which can be clearly distinguished solely because of this relatively very small difference in the highness and frontness of the vowel produced by a speaker.
However, for a speaker of Greek, both of the sounds that might be produced by an English speaker aiming for /ɪ/ or /i:/ would be understood to be variations of the same Greek phoneme. It is extraordinarily rare for a language to have two separate high front vowels. Whether a (typical) Greek speaker listens to a pronunciation of /ɪ/ or /i:/, their language brain will map both sounds onto the Greek I phoneme. So, for example, the words piss and peace will both sound like the word πεις for a Greek speaker, which is the subjunctive of the verb say.
However, if an English speaker wanted to help another non-native speaker hear the difference between the two vowels, there usually is a safe way to do so.
A majority of languages have a high front vowel and a mid front vowel. For a vast majority of speakers these would be thought of as I and E respectively. The I vowel in these languages is typically between English /i:/ and /ɪ/. Greek happens to be one of these languages.
If you want to help such a speaker hear the difference, show them that if you give them a triplet of words such as beat, bit, bet (/bi:t, bɪt, bet/, respectively), they will be able to hear that bit is closer to bet than beat is.
An interesting fact about the phonology of the word been : when it is stressed, or occasionaly when it's the last word in a sentence, it's pronounced /bi:n/—just like the word bean. However, it is usually neither stressed nor the last word in a sentence. In these circumstances, it is usually pronounced /bɪn/—just like the word bin. English is weird, isn't it?