What challenges will an international joint PhD program pose to applicant?
I should preface this by saying I am an Australian living in Germany.

There are many many factors that will define the challenges you as an individual will face, and of course it really depends WHICH countries you are going to spend time in, and where you are from originally. A US/UK joint program for an Australian will not be nearly as tough as a French/Russian program for a Korean.

This is due to what I call "Ausländer tax", which is to say foreigner tax, or put better "outsider tax".
Ausländer tax is an financial, physical and emotional debt that you pay by simply living in a country that you are not native too.

For example, I was paying a moderate Ausländer tax for the first two years of my PhD where every month I would buy a monthly tram ticket to get too and from work. This cost me around $60 a month. After two years I found out there was a special semester tram ticket for students enrolled at the university, which is $90 for the whole semester. After paying this for a year, I then found out that student's don't have to pay for the trams at all if it's before 8am or after 9pm - which pretty much covers 99.9% of my travel times. In essence, I'd paid around $1700 in Ausländer tax for just the trams. Financial Ausländer tax is generally easy to spot. I know i'm paying it by not being able to put in a contribution of my salary towards my pension, for example. I know i'm paying it by being unable to renegotiate my energy bill, because no one at Eon will talk to me in English. I know I pay it every time I get a taxi and speak in English, even though I know very well what the rates should be or the route we should take. Financial Ausländer tax is a bummer but can at least be overcome by being rich.

But Ausländer tax also includes things that are a bit harder to measure, and in cases impossible to overcome. For example, as I cannot speak German to a high standard, walking around town I hear essentially white noise 24/7. People in the street will ask me questions and I won't even know they are talking to me. Sometimes they will be quite offended by this, which makes me feel like shit, and then I have to spend the day at work feeling sorry for myself. Elevator trips are particularly awkward, simply because I have nothing to say. This is 90% a language barrier issue, but 10% a cultural issue, because certain rituals differ from country to country. This constant, unrelenting confusion creates stress and can really wear you down. It is like putting a whale in a zoo. Sure it can survive, and it will generate productive outcomes, but for the whale it is a burden. Worst of all, it's not obvious how to improve the situation for the whale.

There are PLENTY of positives to living abroad however, which I believe outweigh the Ausländer tax certainly for the first few years. You learn the culture, you learn new ways of doing things, and this has a real and practical benefit to you. But after a while, perhaps 2-3 years, these benefits diminish, and the cons of the Ausländer tax accumulate.

The only solution to Ausländer tax is to stop being an Ausländer. To totally integrate with the new culture. This doesn't mean you just learn the new culture - that is what we did in year 1 and 2. It means to adopt the new culture. Redefine yourself and drop the overhead of translating in-and-out of a foreign language/culture by making it your primary language/culture. For some people this is much easier than others, and of course it depends on the cultural delta, but many people never accept this as they are either unable or unwilling to give up their original culture.