Hello Anny welcome to CAF i hope you find the answers you are looking for and the support and friendship CAF has to offer.
I myself am a Roman Catholic and attend Mass at Roman Catholic Mass.I know very little about The Assyrian Church of the East but what i looked up said the following
On November 11, 1994, a historic meeting of Mar Dinkha IV and Pope John Paul II took place in Rome. The two patriarchs signed a document titled Common Christological Declaration between the Catholic Church and the Assyrian Church of the East. One side effect of this meeting was that the Assyrian Church’s relationship to the Chaldean Catholic Church was improved.[20] In 1996, Mar Dinkha IV signed an agreement of cooperation with the Chaldean Patriarch of Baghdad, Raphael I Bidawid, in Southfield, Michigan. In 1997, he entered into negotiations with the Syrian Orthodox Church and the two churches ceased anathematizing each other.
The only difference i read about is…
The lack of the Words of Institution used by Jesus at the Last Supper (“This is my body”…“This is [the cup of] my blood”) in some liturgies of the Church has caused many Western Christians (especially Roman Catholics) to consider them invalid. However, in 2001, after a study of this issue, the Pontifical Council for Promoting Christian Unity and the Congregation for the Doctrine of the Faith (Cardinal Ratzinger, now Benedict XVI, then being prefect) declared that this was a valid liturgy and that Chaldean Catholics could receive the Eucharist in an Assyrian Church if unable to attend their own churches. This declaration was approved by Pope John Paul II.
Im sure others will have more information and eloquent answers for you.God bless